The nature of my inquiry has to do with my work on partisan economic models and automata, and the need to align human and algorithmic intelligence from a moral perspective. To this end, I'm starting with the simplest axioms.

With the understanding that my assumptions may be flawed (leading to this question) it seems to me that the two following examples are algorithmic extensions of the maxim "moderation in all things":

Simple "maximization" and "minimization" are strategies, but not optimal because they only account for a single vector in a two dimensional model; maximax is worse because that it acknowledges downside without seek to mitigate, while minimin borders on the absurd in approaching the question backwards; minimax and maximin are sound, and demonstrably so in an increasing number of contexts. The mechanics of minimax are moderation (as in hedging, mitigation, etc.) as an optimal strategy.

Binary search is a method for optimizing search by going to the middle of an array, and continuing to halve it until the it achieves the desired result. This is literal take on moderation--always choosing the center as an optimization strategy.

The idea I'm drawing from comes from the Temple of Apollo at Delphi:

μηδὲν ἄγαν

"Nothing in excess"

closed as unclear what you're asking by Swami Vishwananda, John Am, Keelan Apr 17 '17 at 10:23

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    Counterargument: If you're in the middle of the road you get run over. "The good is the enemy of the great" to reverse a common piece of wisdom. If you want to just get by, the middle of the road is fine. If you want to excel, at some point you'll have to take a stand. – user4894 Apr 12 '17 at 21:33
  • @user4894 I upvoted your comment. Very good perspective, but not algorithmic. What I'm concerned with is what can be mathematically validated, thus minimax and binary search – DukeZhou Apr 12 '17 at 21:47
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    @user4894 Maybe it will eventually become "Moderation in all things, including moderation" ;) – DukeZhou Apr 12 '17 at 22:15
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    Minimax is a special case of multi-objective optimization. But it is as close to "moderation" as to the idea of "balance", or the Greek ideal of "well rounded man". I do not see how binary search is optimization strategy though, what does it optimize? – Conifold Apr 12 '17 at 23:33
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    I agree with "moderation in all things, including moderation." Interestingly enough, that's terribly hard to make into an algorithmic concept. However, I would point out that the vast majority of uses of min/max I've heard of are not actually an attempt to find a moderate path, but are the result of two competing forces fighting for opposite goals. – Cort Ammon Apr 13 '17 at 0:21